Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1998,106
Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure P is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local P-martingales. We prove that if P exists, it minimizes the reverse relative entropy H(P) over all ELMMs Q for X. A counterexample shows that the assumption of continuity cannot be dropped.